The application of wind energy conversion systems for the production of electrical energy requires a cheap and reliable operation. Especially at high wind velocities fluctuations from the wind field result in large mechanical loads of the wind turbine. Also fluctuations in the grid voltage may yield large dynamic excitations. In order to realize a long lifetime and a reliable operation active control systems are necessary. The main goal of the study described in this thesis is to develop an approach for the design of a high performance control system for a wind turbine with variable speed. The wind turbine system under investigation has a three-bladed rotor which is connected to the generator by a transmission. The electrical conversion system consists of a synchronous generator with a rectifier, direct current transmission and an inverter. The manipulable inputs are the pitch angle of the turbine blades, the field voltage of the generator and the delay angle of the rectifier. Both the generator speed and the direct current are being measured. The control design problem at full load is to minimize fluctuations in speed and current while reducing the mechanical (fatigue) loads. The feedback system should realize this without excessive use of the input variables and must also be simple to implement. I In order to be able to design a high performance control system a high quality dynamic model is required. Much attention has been given to the. modelling of the electrical conversion system. The switching of the thyristors of the rectifier bridge results in periodic behaviour at a high frequency. In order to design a control system an averaged model has been derived through the application of Floquet theory for periodic systems. The properties of the aerodynamic transfer and of the drive train only have been approximately modelled. Deviations of these nominal models from the real system are accounted for using norm-bounded uncertainty models. Using the nominal model and the uncertainty models the control system design has been carried out. The control design problem can suitably be handled by the Linear Quadratic design method. However, instead of using the standard solution with observers, in this study the optimization theory has been applied with respect to a predefined structure of the feedback law. In this approach the order and structure of the controller can be selected as part of the problem formulation. The application to the wind turbine system shows that a high performance control system can be obtained using a relatively simple, low order multivariable feedback law. The use of frequency weighting effectively reduces the role of mechanical parasitic dynamics. Application of the multi-model principle in combination with LQ optimization theory provides a way to synthesize controllers which are robust for large (aerodynamic) changes in operating conditions. A quantitative robustness analysis shows how the design parameters of the feedback law can be adapted in order to enhance the robustness of the controller. The approach taken, involving extensive modelling combined with uncertainty models and with the use of optimization theory and robustness analysis, has been shown to result in a high performance control system. Its main characteristic is the integrated approach of the control problem, with combined control action via the mechanics and the electrical conversion system. It is recommended to apply this integrated approach also to other types of wind turbine systems.